Answer this part on the answer book provided on a fresh page

Q$5$ The switch shown in figure Q$5$a has been in position $"$ a $"$ for a very long time. The circuit

is connected to an oscilloscope as shown in Figure Q$5$a and the scope trace is shown in

Figure Q$5$b$.$ The scope is set as follows: time $()/($div$)=1$ms and $($V$)/($d$)$iv$=2$V$.$ The input to

the circuit is a sinusoidal signal v$\_($s$)($t$)=5$cos$(1000$t$+45\backslash$deg $)$V$.$ Note that the current in the

circuit is taken as the reference signal for the steady state condition.

$($i$)$ What is the average power and the power factor of the circuit?

$($ii$)$ What is the voltage across the capacitor?

$($iii$)$ At t$=0,$ the switch is moved to position $"$ b $".$ Determine the v$\_($C$)($t$)$ for t$>0.$

Figure Q$5$a

Figure Q$5$b

End of part C$.$